Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Here's a question on compound interest and simple interest.

The difference in compound interest and simple interest for 2 years on a sum of money is \$160. If the simple interest for 2 years be \$2,880, the rate percent is ____ ?

How do I do it?

share|improve this question
    
Doesn't this depend on how frequently the interest is compounded? Annually? Monthly? Daily? Continuously? –  MJD Dec 17 '12 at 15:25
    
@MJD the interest is compounded annually... –  ShuklaSannidhya Dec 17 '12 at 15:38
add comment

1 Answer

up vote 0 down vote accepted

Let's call the original principal $P$, and the interest rate $r$. Then the interest accrued in the first year is $Pr$.

If the interest is simple, the interest accrued in the second year is the same, $Pr$ again, for a total of $2Pr$. But if the interest is compound, the interest in the second year is on the original principal plus the first year's interest, $P + Pr$, and so is $(P + Pr)r = Pr + Pr^2$, rather than just $Pr$. The difference between the simple and compound interest accrued in two years is therefore $Pr^2$.

We are given that the simple interest is $2Pr = \$2,880$, and the difference between the two kinds of interest is $Pr^2 = \$160$. Dividing the second by the first gives:

$${ Pr^2\over 2Pr} = {160\over 2880} \\ \frac r2 = \frac1{18}\\ r = \frac19 $$

Or if you prefer, 11.1%.

Then we can solve for the original principal $P$, and then check the values for $P$ and $r$ by calculating the simple and compound interest amounts on $P$ at rate $r$ to see if they match the givens in the question,

share|improve this answer
    
How do we solve for 'P' ? –  ShuklaSannidhya Dec 17 '12 at 16:57
    
How is the difference Pr^2. (Pr+Pr^2-2Pr= Pr^2-Pr)... Shouldn't it be Pr^2-Pr??? –  ShuklaSannidhya Dec 17 '12 at 17:04
    
The simple interest in the first year is $Pr$, and in the second year $Pr$, for a total of $2Pr$. The compound interest in the first year is $Pr$, and in the second year $Pr + Pr^2$, for a total of $2Pr + Pr^2$. You solve for $P$ by taking $2Pr = \$2,880$ and putting in the known value for $r$, leaving an equation in $P$. –  MJD Dec 17 '12 at 17:14
    
thanks a lot Mr. Dominus. –  ShuklaSannidhya Dec 17 '12 at 17:24
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.